Matlab code

The following Matlab code computes the optimal Chebyshev FIR bandpass filter:

M = 101;                           
%normF = [0 0.3 0.4 0.6 0.8 1.0]; % transition bands different
normF = [0 0.3 0.4 0.6 0.7 1.0];  % transition bands the same
amp = [0 0 1 1 0 0];              % desired amplitude in each band

[b2,err2] = remez(M-1,normF,amp); % optimal filter of length M

% REMEZ Parks-McClellan optimal equiripple FIR filter design.
% B=REMEZ(N,F,A) returns a length N+1 linear phase (real, symmetric
% coefficients) FIR filter which has the best approximation to the
% desired frequency response described by F and A in the minimax
% sense. ... REMEZ treats the bands between F(k+1) and F(k+2) for odd
% k as "transition bands" or "don't care" regions.

figure(2);
[H2,freq]=freqz(b2,[1],512);
subplot(2,1,1); plot(freq*10000/pi,20*log10(abs(H2))); grid;
xlabel('Hz'); ylabel('dB'); axis([0 10000 -110 30]);
subplot(2,1,2); plot(freq*10000/pi,20*log10(abs(H2))); grid;
xlabel('Hz'); ylabel('dB'); axis([3500 7000 -0.02 0.02]);

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written by Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.